Journal Article10.1080/10485250108832850
Convergence rates for average square errors for kernel smoothing estimators
Tae Yoon Kim,Dennis D. Cox +1 more
4
TL;DR: Convergence rate of ASE and difference between ISE and ASE are studied, which reveals that curse of dimension affects square errors in regression setting and there exists a cutoff point in dimension where A SE and ISE are no longer asymptotically equivalent.
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Abstract: Until now integrated square error (ISE) for kernel smoothing estimators has been thoroughly investigated in the context of bandwidth selection, while little work has been done for its alternative, average square error (ASE), mainly because ASE and ISE have been regarded to be nearly equivalent. In this paper convergence rate of ASE and difference between ISE and ASE are studied, which reveals that curse of dimension affects square errors in regression setting and there exists a cutoff point in dimension where ASE and ISE are no longer asymptotically equivalent.
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The central limit theorem for degenerate variable U-statistics under dependence
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Uniformly Consistency of the Cauchy-Transformation Kernel Density Estimation Underlying Strong Mixing
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References
A Brief Survey of Bandwidth Selection for Density Estimation
TL;DR: In this article, the authors recommend a "solve-the-equation" plug-in bandwidth selector as being most reliable in terms of overall performance for kernel density estimation.
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Optimal Bandwidth Selection in Nonparametric Regression Function Estimation
TL;DR: In this paper, a bandwidth-selection rule is formulated in terms of cross validation, and under mild assumptions on the kernel and the unknown regression function, it is seen that this rule is asymptotically optimal.
Extent to which least-squares cross-validation minimises integrated square error in nonparametric density estimation
Peter Hall,James Stephen Marron +1 more
TL;DR: In this article, the authors compare different data-driven approaches to the determination of window size, and show that the observable window ĥ� c>>\s performs as well as the so-called "optimal" but unattainable window h>>\s to both first and second order.
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A Comparison of Cross-Validation Techniques in Density Estimation
TL;DR: In this article, a comparison of the Kullback-Leibler and the least-squares cross-validation methods of smoothing parameter selection is made for nonparametric multivariate density estimation.